The easiest way to handle this would simply be to make the changes in the SQL Server directly.
If you need to keep using the Access database you’ll want to upload the changed records to a staging table. Basically a new table with the same name, and without the autonumber (actually called IDENTITY in SQL Server) enabled.
Then use an update statement to update the values in the main table from the values in the staging table.
SET FirstName = StagingTable.FirstName,
LastName = StagingTable.LastName,
WHERE MainTable.IdField = StagingTable.IdField
An UPDATE statement like that one will do the trick. You’ll just need to change the table and column names to your own, and list out all the columns.